As a tree grows, the rate of increase of its height, $h$ m, with respect to time, $t$ years afte

Question

As a tree grows, the rate of increase of its height, $h$ m, with respect to time, $t$ years after planting, is modelled by the differential equation $$\frac{\mathrm{d}h}{\mathrm{d}t} = \frac{1}{10}\sqrt{\left(16 - \frac{1}{2}h\right)}$$ The tree is planted as a seedling of negligible height, so that $h=0$ when $t=0$. State the maximum height of the tree, according to this model.[1] Find an expression for $t$ in terms of $h$, and hence find the time the tree takes to reach half its maximum height.[5]

Accepted Answer

$h_{\max} = 32$ m; $t = 46.9$ years

N2015 P2 Q1

N2015 P2 Q1

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